Prove E field does not depend on dielectric (capacitors)

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SUMMARY

The discussion centers on proving that the electric field (E) between the plates of a large parallel plate capacitor remains constant when the dielectric medium is replaced with a conductive medium. Key equations involved include E = σ/ϵ0 and C = ϵ0A/d. The participant struggled with manipulating these equations to eliminate resistivity (ρ) from the calculations. Ultimately, the conclusion is that the electric field is independent of the dielectric material used between the plates, as long as the capacitor's geometry remains unchanged.

PREREQUISITES
  • Understanding of electric fields and potential difference in capacitors
  • Familiarity with the equations E = σ/ϵ0 and C = ϵ0A/d
  • Knowledge of the concept of dielectric materials and their properties
  • Basic grasp of resistivity (ρ) and its role in electrical circuits
NEXT STEPS
  • Study the derivation of the electric field in capacitors with different dielectric materials
  • Explore the impact of varying plate area (A) and separation distance (d) on capacitance
  • Investigate the behavior of electric fields in conductive media versus dielectric materials
  • Learn about the implications of electric field uniformity in practical capacitor applications
USEFUL FOR

This discussion is beneficial for physics students, electrical engineers, and anyone studying capacitor behavior in different dielectric environments.

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Homework Statement


"Show that the variation of the potential between the plates of a large parallel plate capacitor remains the same if the air between the plates is replaced by a conductive medium."

Homework Equations


E = σ/ϵ0 ; C = ϵ0A/d ' C = Q/V ; E = -dV/dx ; R = ρl/A

The Attempt at a Solution


I've tried a lot of different things, substituting and replacing variables in the equation to try and get ρ to cancel out, but... I honestly have no idea.
 
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Post a couple of the attempts, and maybe someone can point you in the right direction.
 

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